These are notes on the theory of super Riemann surfaces and their moduli spaces, aiming to collect results that are useful for a better understanding of superstring perturbation theory in the RNS formalism.
No abstract is provided for this article.
Inorder tostudy vertex operatorsfortheType IIBsuperstring onAdS space, we derive supersymmetric constraint equations for the vertex operators in AdS3S 3 backgrounds with Ramond-Ramond flux, using Berkovits-Vafa-Witten variables. These constraints are solved to compute the vertex operators and show that they satisfy the linearizedD=6,N=(2;0) equations of motion for a super- gravity and tensor multiplet expanded around theAdS3S 3 spacetime.
We interpret certain strong coupling singularities of the E 8 ×E 8 heterotic string on K3 in terms of exotic six-dimensional theories in which E 8 is a gauge symmetry. These theories are closely related to theories obtained at small instanton singularities, which have E 8 as a global symmetry.
The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N = 4 super Yang-Mills theory in four dimensions.The key ingredients are electric-magnetic duality of gauge theory, mirror symmetry of sigma-models, branes, Wilson and 't Hooft operators, and topological field theory.Seemingly esoteric notions of the geometric Langlands program, such as Hecke eigensheaves and D-modules, arise naturally from the physics.
The problem of quantizing a symplectic manifold (M, ω) can be formulated in terms of the A-model of a complexification of M .This leads to an interesting new perspective on quantization.From this point of view, the Hilbert space obtained by quantization of (M, ω) is the space of (B cc , B ′ ) strings, where B cc and B ′ are two A-branes; B ′ is an ordinary Lagrangian A-brane, and B cc is a space-filling coisotropic A-brane.B ′ is supported on M , and the choice of ω is encoded in the choice of B cc .As an example, we describe from this point of view the representations of the group SL(2, R).Another application is to Chern-Simons gauge theory.
No abstract is provided for this article.
We consider the particle-kink and kink-kink S-matrix elements of the two-dimensional (ψψ)2 model, where the Majorana spinor ψ is an O(N) isovector. Our results confirm many qualitative ideas about the model, including the mass spectrum, the decoupling at N = 4, and the isospinor nature of the kinks.
This lecture surveys a few loosely related topics, ranging from the scarcity of quantum field theories -- and the role that this has played, and still plays, in physics -- to paradoxes involving black holes in soluble two dimensional string theory and the question of whether naked singularities might be of even greater interest to string theorists than black holes.
In ordinary quantum field theory, one can define the algebra of observables in a given region in spacetime, but in the presence of gravity, it is expected that this notion ceases to be well-defined. A substitute that appears to make sense in the presence of gravity and that also is more operationally meaningful is to consider the algebra of observables along the timelike worldline of an observer. It is known that such an algebra can be defined in quantum field theory, and the timelike tube theorem of quantum field theory suggests that such an algebra is a good substitute for what in the absence of gravity is the algebra of a region. The static patch in de Sitter space is a concrete example in which it is useful to think in these terms and to explicitly incorporate an observer in the description.
This paper is devoted to a systematic discussion of the supersymmetric index Tr (-1)^F for the minimal supersymmetric Yang-Mills theory -- with any simple gauge group G -- primarily in four spacetime dimensions. The index has refinements that probe confinement and oblique confinement and the possible spontaneous breaking of chiral symmetry and of global symmetries, such as charge conjugation, that are derived from outer automorphisms of the gauge group. Predictions for the index and its refinements are obtained on the basis of standard hypotheses about the infrared behavior of gauge theories. The predictions are confirmed via microscopic calculations which involve a Born-Oppenheimer computation of the spectrum as well as mathematical formulas involving triples of commuting elements of G and the Chern-Simons invariants of flat bundles on the three-torus.
This article consists of a very short introduction to classical and quantum information theory. Basic properties of the classical Shannon entropy and the quantum von Neumann entropy are described, along with related concepts such as classical and quantum relative entropy, conditional entropy, and mutual information. A few more detailed topics are considered in the quantum case.
No abstract is provided for this article.
It has been argued based on electric-magnetic duality and other ingredients that the Jones polynomial of a knot in three dimensions can be computed by counting the solutions of certain gauge theory equations in four dimensions. Here, we attempt to verify this directly by analyzing the equations and counting their solutions, without reference to any quantum dualities. After suitably perturbing the equations to make their behavior more generic, we are able to get a fairly clear understanding of how the Jones polynomial emerges. The main ingredient in the argument is a link between the four-dimensional gauge theory equations in question and conformal blocks for degenerate representations of the Virasoro algebra in two dimensions. Along the way we get a better understanding of how our subject is related to a variety of new and old topics in mathematical physics, ranging from the Bethe ansatz for the Gaudin spin chain to the $M$-theory description of BPS monopoles and the relation between Chern-Simons gauge theory and Virasoro conformal blocks.
